On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions


Authors

Arshad Ali - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan. Faranak Rabiei - Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. - Institute For Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. Kamal Shah - Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan.


Abstract

In this manuscript, using Schaefer's fixed point theorem, we derive some sufficient conditions for the existence of solutions to a class of fractional differential equations (FDEs). The proposed class is devoted to the impulsive FDEs with nonlinear integral boundary condition. Further, using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss various kinds of Ulam-Hyers stability. Finally to illustrate the established results, we provide an example.


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